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Using data from 20 compact cars, a consumer group develops a model that predicts the stopping time for a vehicle by using its weight. You consider using this model to predict the stopping time for your large SUV. Explain why this is not advisable.

A regression of Total Revenue on Ticket Sales by the concert production company of Exercises 2 and 4 finds the model $$\text { Revenue }=-14,228+36.87 \text { Ticket Sales. }$$ a. Management is considering adding a stadium-style venue that would seat \(10,000 .\) What does this model predict that revenue would be if the new venue were to sell out? b. Why would it be unwise to assume that this model accurately predicts revenue for this situation?

GPA An athletic director proudly states that he has used the average GPAs of the university's sports teams and is predicting a high graduation rate for the teams. Why is this method unsafe?

In justifying his choice of a model, a student wrote, "I know this is the correct model because \(R^{2}=99.4 \%\) a. Is this reasoning correct? Explain. b. Does this model allow the student to make accurate predictions? Explain.

A student who has created a linear model is disappointed to find that her \(R^{2}\) value is a very low \(13 \%\). a. Does this mean that a linear model is not appropriate? Explain. b. Does this model allow the student to make accurate predictions? Explain.

Suppose a researcher studying health issues measures blood pressure and the percentage of body fat for several adult males and finds a strong positive association. Describe three different possible cause-andeffect relationships that might be present.

To measure progress in reading ability, students at an elementary school take a reading comprehension test every year. Scores are measured in "grade-level" units; that is, a score of 4.2 means that a student is reading at slightly above the expected level for a fourth grader. The school principal prepares a report to parents that includes a graph showing the me 37 ?. a. The graph shows that, on average, students progress at about one reading level per year. This graph shows averages for each grade. The linear trend has been enhanced by using averages. b. Very close to 1. c. The individual data points would show much more scatter, and the correlation would be lower. d. A slope of 1 would 37 ?. a. The graph shows that, on average, students progress at about one reading level per year. This graph shows averages for each grade. The linear trend has been enhanced by using averages. b. Very close to 1. c. The individual data points would show much more scatter, and the correlation would be lower. d. A slope of 1 would indicate that for each 1-year grade level increase, the average reading level is increasing by 1 year. indicate that for each 1-year grade level increase, the average reading level is increasing by 1 year.an reading score for each grade. In his comments, he points out that the strong positive trend demonstrates the success of the school's reading program. a. Does this graph indicate that students are making satisfactory progress in reading? Explain. b. What would you estimate the correlation between Grade and Average Reading Level to be? c. If, instead of this plot showing average reading levels, the principal had produced a scatterplot of the reading levels of all the individual students, would you expect the correlation to be the same, higher, or lower? Explain. d. Although the principal did not do a regression analysis, someone as statistically astute as you might do that. (But don't bother.) What value of the slope of that line would you view as demonstrating acceptable progress in reading comprehension? Explain.

People swam across Lake Ontario from Niagara-on-the-Lake to Toronto (52 km, or about 32.3 mi) 62 times between 1954 and \(2016 .\) We might be interested in whether the swimmers are getting any faster or slower. Here are the regression of the crossing Times (minutes) against the Year since 1954 of the crossing and a plot of the residuals against Year since 1954: a. What does the \(R^{2}\) mean for this regression? b. Are the swimmers getting faster or slower? Explain. c. The outlier seen in the residuals plot is a crossing by Vicki Keith in 1987 in which she swam a round trip, north to south, and then back again. Clearly, this swim doesn't belong with the others. Would removing it change the model a lot? Explain.